If G = 6.67x10-11Nm2kg-2 and the mass of the Earth is 6.0x1024kg, calculate the potential at the surface of the Earth if the radius of the Earth is 6.4x106m.

Answer

The potential (Ep per kg) at the surface of the Earth is

- 63 MJ kg -1

Do 10 MJ kg-1 of work on raising an object from the Earth's surface and it will move up to a point where it's potential is - 53MJ kg-1. That's 10 MJ kg-1 greater than on the surface because it is 10MJ kg-1 closer to zero.

Confusing! Look at the following diagram. It shows how potential drops as you move further from the surface of the Earth.

So we can define potential as "the work done per kg by an object when it moves from infinity to a point in a field".

Looking back at the example above, that means that if you let 1kg drop from infinity to the surface of the Earth it will lose 63MJ of potential energy. Ignore air resistance, and the object will have that much kinetic energy when it hits the surface of the planet.